Removable Singularities For Kahler Metrics With Constant Holomorphic Sectional Curvature

In the dissertation,we study the local removability of the singularities of a Kah-ler metric with constant holomorphic sectional curvature,which is the special case of the local Hermitian symmetric space.Let B Bn(?)Cn be the unit ball,K a subset of Bn,and g the KShler metric with constant holomorphic sectional curvature on Bn\K.In the dissertation,we use the Kahler version of Cartan-Ambrose-Hicks theorem and Thurston’s[1]general theory of developing maps to prove the existence of the devel-oping map with the image in the space form on Bn\K,and then apply the extension theorem of the holomorphic mapping to prove that the developing map can be extended to B" and is non-degenerate everywhere when K is a compact set or a subvariety with codimension greater than or equal to two.Finally through pulling back the standard metric by the developing map,we get an extension of the metric.The dissertation also proves the uniqueness of the extension.This dissertation provides an inspiration for the study of the existence of develop-ing maps on the local Hermitian symmetric space,and also lays a foundation for the later research of the Kahler-Einstein metric with singularities along a divisor,using the developing map.